Let’s start by stating the obvious: Purgatory is not only the setting, but also the subject matter of the second cantica of Dante’s Divine Comedy. The idea behind Purgatory is that no matter how badly a person sins in life, he can still save his soul by repenting before death.
Instead of going to Hell and suffering eternal damnation, the saved soul thus gets a ticket to Purgatory, where it remains until purged of all its vices. Here’s where the idea of cleanliness comes in. The word “purgatory” is related to the verb “to purge,” meaning to clean or purify. “Purge” has its roots in the word “pure.” So Purgatory is above all a place of education, where the saved souls learn to purify their souls of all the vices they have picked up in life. When the soul is perfectly clean, the gates of Heaven open for it.
As you read through the text, you’ll find that many of the penitents (inhabitants of Purgatory, as opposed to the “sinners” of Hell) have repented prior to their arrival in Purgatory. Ironically, many of the characters inhabiting Purgatory are people that medieval readers would likely have considered completely evil and would’ve expected to find in the Inferno. Scandalous.
Seriously, Dante is known for thwarting expectations; this is his way of showcasing his greatness as a poet and logician. He can take these depraved figures, speculate about their repentance, save them, and then show off their good aspects in Purgatorio.
Theatrics aside, Purgatorio is ultimately about hope. More than the other part of the Divine Comedy, it speaks to living readers because it shows imperfect individuals striving in good faith to become virtuous. Which is really what many of us are trying to do in our own lives here on earth. Unlike the hopelessly corrupt souls in Hell or the perfect souls in Heaven, Purgatory allows for the possibility of self-improvement, showing that against all odds, man really can change for the better. This promise of salvation is ultimately what keeps us coming back to Purgatorio.